Forecasting long range dependent time series with exogenous variable using ARFIMAX model

Abstract

Time series analysis and forecasting is one of the challenging issues of statistical modelling. Modelling of price and forecasting is a vital matter of concern for both the farming community and policy makers, especially in agriculture. Many practical agricultural data, principally commodity price data shows the typical feature of long memory process or long range dependency. For capturing the long memory behavior of the data Autoregressive Fractionally Integrated Moving Average (ARFIMA) model is generally used. Sometimes, in time series data besides the original series, data on some auxiliary or exogenous variables may be available or can be made available with a lower cost; like besides the market prices of commodities, market arrivals for that commodity may be available and it affects the market price of commodities. This type of exogenous variable may be incorporated in existing model to improve the model performance and forecasting accuracy, like Autoregressive Fractionally Integrated Moving Average with exogenous variables (ARFIMAX) model. In the present study undertaken at ICAR-IASRI, New Delhi during 2019, daily maximum and modal price of potato of Agra market of UP, India are taken along with daily market arrival. Both the ARFIMA and ARFIMAX model with market arrival as exogenous variable are applied for the data under study. Comparative studies of the fitted models are employed by using the Relative Mean Absolute Percentage Error (RMAPE) and Root Mean Square Error (RMSE) criteria. We could establish superiority of the ARFIMAX model over the ARFIMA model in terms of modeling and forecasting efficiency.